Rigid-body Control Research Articles

Robust Distance-Based Formation Control of Multiple Rigid Bodies with Orientation Alignment

This paper addresses the problem of distance- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in 3D space, under static and undirected communication topologies. More specifically, we design a decentralized model-free control protocol in the sense that each agent uses only local information from its neighbors to calculate its own control signal, without incorporating any knowledge of the model nonlinearities and exogenous disturbances. Moreover, the transient and steady state response is solely determined by certain designer-specified performance functions and is fully decoupled by the agents’ dynamic model, the control gain selection, the underlying graph topology as well as the initial conditions. Additionally, by introducing certain inter-agent distance constraints, we guarantee collision avoidance and connectivity maintenance between neighboring agents. Finally, simulation results verify the performance of the proposed controllers.

Launch vehicle design and GNC sizing with ASTOS

The European Space Agency (ESA) is currently involved in several activities related to launch vehicle designs (Future Launcher Preparatory Program, Ariane 6, VEGA evolutions, etc.). Within these activities, ESA has identified the importance of developing a simulation infrastructure capable of supporting the multi-disciplinary design and preliminary guidance navigation and control (GNC) design of different launch vehicle configurations. Astos Solutions has developed the multi-disciplinary optimization and launcher GNC simulation and sizing tool (LGSST) under ESA contract. The functionality is integrated in the Analysis, Simulation and Trajectory Optimization Software for space applications (ASTOS) and is intended to be used from the early design phases up to phase B1 activities. ASTOS shall enable the user to perform detailed vehicle design tasks and assessment of GNC systems, covering all aspects of rapid configuration and scenario management, sizing of stages, trajectory-dependent estimation of structural masses, rigid and flexible body dynamics, navigation, guidance and control, worst case analysis, launch safety analysis, performance analysis, and reporting.

Guidance and Attitude Control of Unstable Rigid Bodies With Single-Use Thrusters

In this paper, we introduce a novel computationally efficient and practical algorithm for robust guidance and attitude control of unstable rigid bodies using the discrete fixed-magnitude, fixed-duration actuation representative of single-use thrusters. New guidance and attitude continuous control laws are developed based on the nonlinear rigid-body motion model, where the objective is to intercept a target and maintain the near zero angle of attack. A methodology is then introduced to adapt the continuous control system to discrete impulsive forces with constant magnitude and duration. An actuation management scheme is presented based on the equivalence of the total impulse of the continuous control law and thruster force. Realistic time delays and noise distributions are included in a sensor fusion algorithm based on the extended Kalman filter. Simultaneous control for course corrections to ensure the target interception and stabilization of the vehicle attitude is presented through Monte Carlo simulations with various uniformly distributed direction and velocity errors.

Attitude control of rigid body with inertia uncertainty and saturation input

In this paper, the attitude control problem of rigid body is addressed with considering inertia uncertainty, bounded time-varying disturbances, angular velocity-free measurement, and unknown non-symmetric saturation input. Using a mathematical transformation, the effects of bounded time-varying disturbances, uncertain inertia, and saturation input are combined as total disturbances. A novel finite-time observer is designed to estimate the unknown angular velocity and the total disturbances. For attitude control, an observer-based sliding-mode control protocol is proposed to force the system state convergence to the desired sliding-mode surface; the finite-time stability is guaranteed via Lyapunov theory analysis. Finally, a numerical simulation is presented to illustrate the effective performance of the proposed sliding-mode control protocol.

Sliding Mode Active Vibration Control and Three Axis Attitude Control using Four Reaction Wheels

The most important problems in satellites are their energy supply and decreasing weight. One of the solutions is using flexible appendages. Flexibility can supply both energy and weight loss in satellites. Also other appendages like antennas and mechanical arms can be flexible. But flexibility can produce some vibrations. These vibrations cause complexity attitude control systems due to flexible appendages. In this paper, the attitude control of flexible satellite by using four reaction wheels in presence of gravity gradient and orbit frequency has been considered. The dynamic of flexible appendages have been derived from energy equations and Lagrange method. Also, momentum management and minimization of the momentum have been employed to avoid of reaction wheels saturation. Then, the control command law using the quaternion error vector for attitude control of rigid body and sliding mode control (SMC) for active suppuration of flexible appendages have been used. Finally the performance of control system between presence and absence of reaction wheels has been compared.

Attitude control of multiple rigid bodies with uncertainties and disturbances

Decentralized attitude synchronization and tracking control for multiple rigid bodies are investigated in this paper. In the presence of inertia uncertainties and environmental disturbances, we propose a class of decentralized adaptive sliding mode control laws. An adaptive control strategy is adopted to reject the uncertainties and disturbances. Using the Lyapunov approach and graph theory, it is shown that the control laws can guarantee a group of rigid bodies to track the desired time-varying attitude and angular velocity while maintaining attitude synchronization with other rigid bodies in the formation. Simulation examples are provided to illustrate the feasibility and advantage of the control algorithm.

Existence of variationally defined curves with higher order elliptic Lagrangians

We present a method for proving the existence of solutions to a class of one dimensional variational problems, namely those where the Lagrangian is strongly elliptic. The method is demonstrated by some examples of optimal interpolation problems which are motivated by applications to the mechanics and control of rigid bodies. In each case the key step is to show that the variational problem satisfies the Palais–Smale condition. We do so in a general setting, showing that the number of initial conditions required depends on the higher order energy bounding properties of the Lagrangian.

On the formulation of cost functions for torque-optimized control of rigid bodies

In the context of controlling the attitude of a rigid body, this communique uses recent results on representations of torques (moments) to establish cost functions. The resulting cost functions are both properly invariant under whatever choice of Euler angles is used to parameterize the rotation of the rigid body and have transparent physical interpretations. The function is related to existing works in geometric control theory and applications of optimal control theory to biomechanical systems.

Constrained rigid body stability and control

Stability and control of a single or three-body constrained system are considered. Several different types of constrained motion are among them: the impact phase of a free body colliding with the ground, contact with a stationary or moving platform, movement on a frictionless surface or multiple rigid bodies connected by holonomic constraints, and moving as in the human arm. The single body constrained system is controlled by sliding mode control. The stability of the three-link arm at arbitrary equilibrium points and Lyapunov stability in the vicinity of the equilibrium point are formulated. The formulation and derivations are by computational tools, that is, state space analysis and matrices. The approach can easily be extended to larger systems with many rigid bodies such as skeletal systems. The formulation minimizes human labor in formulations and simulations. The sliding mode behavior of the model on a frictionless surface and the three link arm stability are demonstrated via simulation. Challenges for application to natural systems are outlined. Copyright © 2014 John Wiley & Sons, Ltd.

Distributed event-triggered cooperative attitude control of multiple rigid bodies with leader–follower architecture

In this note, the distributed event-triggered cooperative attitude control of multiple rigid bodies with leader–follower architecture is investigated, where both the cases of static and dynamic leaders are all considered. Two distributed triggering procedures are first introduced for the followers and leaders, and then the distributed cooperative controllers are designed under the proposed triggering schemes. Under the designed controllers with the event-triggered strategies, it is shown that the orientations of followers converge to the convex hull formed by the desired leaders’ orientations with zero angular velocities. Moreover, the communication pressure in network is reduced and the energy of each agent is saved. Simulation results show the effectiveness of the proposed method.

Adjoint assisted geometry design of a feedback controlled missile

A novel optimisation framework using an adjoint cost sensitivity calculation, and integrating computer simulations of fluid dynamics, rigid body dynamics and control is proposed. A generic tail-fin steered missile under closed-loop control is used to show that the framework is able to generate a detailed geometrical tail-fin design and tune control performance parameters that are directly related to the range and manoeuvrability of the missile. It is shown that this new methodology is able to reduce the aerodynamic drag by 2% and the tracking error by about 3% relative to the original design.

Coordinated attitude motion control of multiple rigid bodies on manifold SO (3)

As a special case of consensus on non-linear spaces, in this study coordinated attitude motion control for a group of rigid bodies is investigated for second-order systems on Lie group SO(3). By introducing an auxiliary variable for each rigid body, the distributed controllers are designed so that the left-invariant coordination is asymptotically achieved and total coordination is at least locally asymptotically achieved. Simulation results for a multi-agent system consist of four rigid bodies show the effectiveness of the proposed design.

Dynamic modeling and control design for a parallel-mechanism-based meso-milling machine tool

SUMMARYA novel rigid-body control design methodology for 6-degree-of-freedom (dof) parallel kinematic mechanisms (PKMs) is proposed. The synchronous control of PKM joints is addressed through a novel formulation of contour and lag errors. Robust performance as a control specification is addressed. A convex combination controller design approach is applied to address the problem of simultaneously satisfying multiple closed-loop specifications. The applied dynamic modeling approach allows the design methodology to be extended to 6-dof spatial PKMs. The methodology is applied to the design of a 6-dof PKM-based meso-milling machine tool and simulations are conducted.

Passivity Based Attitude Control of Rigid Bodies

AbstractIn this paper, we present a tutorial on passivity based attitude control that has been investigated over the past two decades. Both regulation control and adaptive tracking control for the attitude motion of rigid bodies are discussed under a unified passivity framework. Our attention is mainly confined to the attitude control schemes that are based on the passivity notion. Output feedback attitude control, attitude synchronization, and some open problems are also discussed.

On the stability and stabilization of quaternion equilibria of rigid bodies

We study attitude control of rigid bodies on quaternion coordinates under three mathematically different perspectives, depending on how the system dynamics are assumed to evolve. In the first case, we suppose that one equilibrium point is chosen a priori and a continuous controller is used under the assumption that the rigid body always spins in the same direction. In the second case, we relax the assumption that the sense of rotation is constant. Finally, a third scenario is considered in which hybrid (switching) control is used to choose the direction in which to spin, that is, both equilibria are continuously considered with regard to less energy consumption. It is showed that each of three scenarios must be treated in a different theoretical setting. A comparative study in simulations is also provided.

Coordinating control of multiple rigid bodies based on motion primitives

This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and maneuvers, are given as building blocks for generating coordinated motions. In a motion-primitive based planning framework, a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturbations. The control method combines the relative equilibria stabilization with maneuver design, and results in a close-loop motion planning framework. The performance of the control method has been illustrated through a numerical simulation.

A unified approach to rigid body rotational dynamics and control

This paper develops a unified methodology for obtaining both the general equations of motion describing the rotational dynamics of a rigid body using quaternions as well as its control. This is achieved in a simple systematic manner using the so-called fundamental equation of constrained motion that permits both the dynamics and the control to be placed within a common framework. It is shown that a first application of this equation yields, in closed form, the equations of rotational dynamics, whereas a second application of the self-same equation yields two new methods for explicitly determining, in closed form, the nonlinear control torque needed to change the orientation of a rigid body. The stability of the controllers developed is analysed, and numerical examples showing the ease and efficacy of the unified methodology are provided.

Bounded attitude control of rigid bodies: Real-time experimentation to a quadrotor mini-helicopter

A quaternion-based feedback is developed for the attitude stabilization of rigid bodies. The control design takes into account a priori input bounds and is based on nested saturation approach. It results in a very simple controller suitable for an embedded use with low computational resources available. The proposed method is generic not restricted to symmetric rigid bodies and does not require the knowledge of the inertia matrix of the body. The control law can be tuned to force closed-loop trajectories to enter in some a priori fixed neighborhood of the origin in a finite time and remain thereafter. The global stability is guaranteed in the case where angular velocity sensors have limited measurement range. The control law is experimentally applied to the attitude stabilization of a quadrotor mini-helicopter.

Cooperative Attitude Control of Multiple Rigid Bodies with Multiple Time-Varying Delays and Dynamically Changing Topologies

Cooperative attitude regulation and tracking problems are discussed in the presence of multiple time-varying communication delays and dynamically changing topologies. In the case of cooperative attitude regulation, we propose conditions to guarantee the stability of the closed-loop system when there exist multiple time-varying communication delays. In the case of cooperative attitude tracking, the result of uniformly ultimate boundedness of the closed-loop system is obtained when there exist both multiple time-varying communication delays and dynamically changing topologies. Simulation results are presented to validate the effectiveness of these conclusions.

Tactics‐Based Behavioural Planning for Goal‐Driven Rigid Body Control

Abstract Controlling rigid body dynamic simulations can pose a difficult challenge when constraints exist on the bodies' goal states and the sequence of intermediate states in the resulting animation. Manually adjusting individual rigid body control actions (forces and torques) can become a very labour‐intensive and non‐trivial task, especially if the domain includes a large number of bodies or if it requires complicated chains of inter‐body collisions to achieve the desired goal state. Furthermore, there are some interactive applications that rely on rigid body models where no control guidance by a human animator can be offered at runtime, such as video games. In this work, we present techniques to automatically generate intelligent control actions for rigid body simulations. We introduce sampling‐based motion planning methods that allow us to model goal‐driven behaviour through the use of non‐deterministic Tactics that consist of intelligent, sampling‐based control‐blocks, called Skills. We introduce and compare two variations of a Tactics‐driven planning algorithm, namely behavioural Kinodynamic Rapidly Exploring Random Trees (BK‐RRT) and Behavioural Kinodynamic Balanced Growth Trees (BK‐BGT). We show how our planner can be applied to automatically compute the control sequences for challenging physics‐based domains and that is scalable to solve control problems involving several hundred interacting bodies, each carrying unique goal constraints.